The quality of conventional mammograms is limited in contrast by the large fraction of scattered photons and the low inherent contrast of the tissues of the breast, and in resolution by geometric unsharpness determined by finite x-ray focal spot size. Better system resolution and contrast will allow earlier and more reliable diagnosis of malignancies, with a resulting reduction in mortality. Breast cancer is currently the leading cause of non-preventable cancer death in American women. Kumakhov capillary optics, small bundles of hollow capillary tubes, enable the manipulation of x-rays in ways which were not previously possible. The use of Kumakhov capillary optics in place of conventional scatter-reduction grids would increase scatter rejection, and increase the transmission of primary photons, and thus reducing patient dose. They would often greatly reduce the problem of geometric unsharpness, and therefore increase system resolution and enable the use of primary digital detectors. During Phase I, extensive calculations and measurements of the performance of Kumakhov capillary optics will be performed at photon energies and in geometries appropriate for mammographic systems. The goal of Phase I is an optimized preliminary design of a Kumakhov capillary optical system for mammography.